Estimating the location of a wireless terminal based on the traits of the multipath components of a signal

ABSTRACT

A technique for estimating the location of a wireless terminal at an unknown location in a geographic region is disclosed. The technique is based on the recognition that there are traits of electromagnetic signals that are dependent on topography, the receiver, the location of the transmitter, and other factors. For example, if a particular radio station is known to be received strongly at a first location and weakly at a second location, and a given wireless terminal at an unknown location is receiving the radio station weakly, it is more likely that the wireless terminal is at the second location than at the first location.

FIELD OF THE INVENTION

The present invention relates to telecommunications in general, and,more particularly, to a technique for estimating the location of awireless terminal and using the estimate of the location in alocation-based application.

BACKGROUND

FIG. 1 depicts a diagram of the salient components of wirelesstelecommunications system 100 in accordance with the prior art. Wirelesstelecommunications system 100 comprises: wireless terminal 101, basestations 102-1, 102-2, and 102-3, wireless switching center 111,assistance server 112, location client 113, and Global PositioningSystem (“GPS”) constellation 121. Wireless telecommunications system 100provides wireless telecommunications service to all of geographic region120, in well-known fashion.

The salient advantage of wireless telecommunications over wirelinetelecommunications is the mobility that is afforded to the users. On theother hand, the salient disadvantage of wireless telecommunications liesin that fact that because the user is mobile, an interested party mightnot be able to readily ascertain the location of the user.

Such interested parties might include both the user of the wirelessterminal and remote parties. There are a variety of reasons why the userof a wireless terminal might be interested in knowing his or herlocation. For example, the user might be interested in telling a remoteparty where he or she is or might seek advice in navigation.

In addition, there are a variety of reasons why a remote party might beinterested in knowing the location of the user. For example, therecipient of an E 9-1-1 emergency call from a wireless terminal might beinterested in knowing the location of the wireless terminal so thatemergency services vehicles can be dispatched to that location.

There are many techniques in the prior art for estimating the locationof a wireless terminal.

In accordance with one technique, the location of a wireless terminal isestimated to be at the center of the cell or centroid of the sector inwhich the wireless terminal is located. This technique is advantageousin that it does not require that additional hardware be added to thewireless terminal or to the wireless telecommunications system, and,therefore, the first technique can be inexpensively implemented inlegacy systems. The first technique is only accurate (in presentcellular systems), however, to within a few kilometers, and, therefore,it is generally not acceptable for applications (e.g., emergencyservices dispatch, etc.) that require higher accuracy.

In accordance with a second technique, the location of a wirelessterminal is estimated by triangulating the angle of arrival ormultilaterating the time of arrival of the signals transmitted by thewireless terminal. This technique can achieve accuracy to within a fewhundreds of meters and is advantageous in that it can be used withlegacy wireless terminals. The disadvantage of this second technique,however, is that it generally requires that hardware be added to thetelecommunication system's base stations, which can be prohibitivelyexpensive.

In accordance with a third technique, the location of a wirelessterminal is estimated by a radio navigation unit, such as, for example,a Global Positioning System (GPS) receiver, that is incorporated intothe wireless terminal. This technique is typically accurate to withintens of meters but is disadvantageous in that it does not workconsistently well indoors, in heavily wooded forests, or in urbancanyons. Furthermore, the accuracy of this third technique can beseverely degraded by multipath reflections.

Therefore, the need exists for a technique for estimating the locationof a wireless terminal with higher resolution than the first techniqueand without some of the costs and disadvantages of the second and thirdtechniques.

SUMMARY OF THE INVENTION

The present invention enables the construction and use of a system thatcan estimate the location of a wireless terminal without some of thecosts and limitations associated with techniques for doing so in theprior art.

The present invention is based on the recognition that there are traitsof electromagnetic signals that are dependent on topography, thereceiver, the location of the transmitter, and other factors. Forexample, if a particular radio station is known to be received stronglyat a first location and weakly at a second location, and a givenwireless terminal at an unknown location is receiving the radio stationweakly, it is more likely that the wireless terminal is at the secondlocation than at the first location.

By quantifying “strongly” and “weakly” and extending this principle tomultiple traits and multiple signals, the present invention can estimatethe location of a wireless terminal with greater accuracy.

The illustrative embodiment comprises estimating the location of awireless terminal based on a measured temporal difference of a pair ofmultipath components of a signal as processed by said wireless terminal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a map of a portion of a wireless telecommunicationssystem in the prior art.

FIG. 2 depicts a diagram of the salient components of wirelesstelecommunications system 200 in accordance with the illustrativeembodiment of the present invention.

FIG. 3 depicts a block diagram of the salient components of locationserver 214, as shown in FIG. 2, in accordance with the illustrativeembodiment.

FIG. 4 depicts a flowchart of the salient processes performed inaccordance with the illustrative embodiment of the present invention.

FIG. 5 depicts a flowchart of the salient processes performed inaccordance with process 401 of FIG. 4: building Location-Trait Database313.

FIGS. 6 a through 6 k depict geographic regions and their deconstructioninto a plurality of locations.

FIG. 6L depicts an alternative partitioning of geographic region 220into 64 square locations.

FIG. 6 m depicts a graphical representation of an adjacency graph ofgeographic region 220 as partitioned in FIGS. 6 c through 6 e.

FIG. 6 n depicts a graphical representation of an adjacency graph of thehighway intersection partitioned in FIGS. 6 h through 6 k.

FIG. 7 depicts a flowchart of the salient processes performed as part ofprocess 402 of FIG. 4: populating Trait-Correction Database 313.

FIGS. 8 a through 8 c depict illustrative distortion and correctioncurves.

FIG. 9 depicts a flowchart of the salient processes performed in process403 (of FIG. 4): maintaining Location-Trait Database 313.

FIG. 10 depicts a flowchart of the salient processes performed inprocess 701 of FIG. 7: estimating the location of wireless terminal 201.

FIG. 11 a depicts a flowchart of the salient processes performed inprocess 901 of FIG. 9: generating the probability distribution for thelocation of wireless terminal 201 based on the traits of one or moresignals received by, or transmitted to, wireless terminal 201 atinstants H₁ through H_(Y).

FIG. 11 b depicts a flowchart of the salient processes performed inaccordance with process 1104 of FIG. 11 a: search area reduction.

FIG. 11 c depicts a flowchart of the salient processes performed inaccordance with process 1105: generating the probability distributionfor that wireless terminal 201 at each of instants H₁ through H_(Y).

FIG. 12 depicts a flowchart of the salient processes performed inprocess 902 of FIG. 9: generating the probability distribution for thelocation of wireless terminal 201 based on GPS-derived information(i.e., information from GPS constellation 221).

FIG. 13 depicts a flowchart of the salient processes performed inprocess 903 of FIG. 9: combining non-GPS-based and GPS-based probabilitydistributions for the location of wireless terminal 201.

FIG. 14 depicts a first example of combining non-GPS-based instants H₁through H_(Y) and GPS-based instants G₁ through G_(Z) into compositeinstants J₁ through J_(F).

FIG. 15 depicts a second example of combining non-GPS-based instants H₁through H_(Y) and GPS-based instants G₁ through G_(Z) into compositeinstants J₁ through J_(F).

DETAILED DESCRIPTION

For the purposes of this specification, the following terms and theirinflected forms are defined as follows:

-   -   The term “location” is defined as a one-dimensional point, a        two-dimensional area, or a three-dimensional volume.    -   The term “staying probability” is defined as an estimate of the        probability P_(S)(b, T, N, W) that wireless terminal W in        location b at calendrical time T will still be in location b at        time T+Δt, given environmental conditions, N.    -   The term “moving probability” is defined as an estimate of the        probability P_(M)(b, T, N, W, c) that wireless terminal W in        location b at calendrical time T will be in adjacent location c        at time T+Δt, given environmental conditions, N.    -   The term “environmental conditions N,” are defined to include        one or more physical aspects of the environment, and includes,        but is not limited to, the weather, the astronomical conditions,        atmospheric conditions, the quantity and density of radio        traffic, the quantity and density of vehicular traffic, road and        sidewalk construction, etc.    -   The term “calendrical time T” is defined as the time as        denominated in one or more measures (e.g., seconds, minutes,        hours, time of day, day, day of week, month, month of year,        year, etc.).

Overview—FIG. 2 depicts a diagram of the salient components of wirelesstelecommunications system 200 in accordance with the illustrativeembodiment of the present invention. Wireless telecommunications system200 comprises: wireless terminal 201, base stations 202-1, 202-2, and202-3, wireless switching center 211, assistance server 212, locationclient 213, location server 214, and GPS constellation 221, which areinterrelated as shown. The illustrative embodiment provides wirelesstelecommunications service to all of geographic region 220, inwell-known fashion, estimates the location of wireless terminal 201within geographic region 220, and uses that estimate in a location-basedapplication.

In accordance with the illustrative embodiment, wirelesstelecommunications service is provided to wireless terminal 201 inaccordance with the Universal Mobile Telecommunications System, which iscommonly known as “UMTS.” After reading this disclosure, however, itwill be clear to those skilled in the art how to make and usealternative embodiments of the present invention that operate inaccordance with one or more other air-interface standards (e.g., GlobalSystem Mobile “GSM,” CDMA-2000, IS-136 TDMA, IS-95 CDMA, 3G WidebandCDMA, IEEE 802.11 WiFi, 802.16 WiMax, Bluetooth, etc.) in one or morefrequency bands.

Wireless terminal 201 comprises the hardware and software necessary tobe UMTS-compliant and to perform the processes described below and inthe accompanying figures. For example and without limitation, wirelessterminal 201 is capable of:

-   -   i. measuring one or more traits of one of more electromagnetic        signals and of reporting the measurements to location server        214, and    -   ii. transmitting one or more signals and of reporting the        transmission parameters of the signals to location server 214,        and    -   iii. receiving GPS assistance data from assistance server 212 to        assist it in acquiring and processing GPS ranging signals.        Wireless terminal 201 is mobile and can be at any location        within geographic region 220. Although wireless        telecommunications system 200 comprises only one wireless        terminal, it will be clear to those skilled in the art, after        reading this disclosure, how to make and use alternative        embodiments of the present invention that comprise any number of        wireless terminals.

Base stations 202-1, 202-2, and 202-3 communicate with wirelessswitching center 211 and with wireless terminal 201 via radio inwell-known fashion. As is well known to those skilled in the art, basestations are also commonly referred to by a variety of alternative namessuch as access points, nodes, network interfaces, etc. Although theillustrative embodiment comprises three base stations, it will be clearto those skilled in the art, after reading this disclosure, how to makeand use alternative embodiments of the present invention that compriseany number of base stations.

In accordance with the illustrative embodiment of the present invention,base stations 202-1, 202-2, and 202-3 are terrestrial, immobile, andwithin geographic region 220. It will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which some or all of the basestations are airborne, marine-based, or space-based, regardless ofwhether or not they are moving relative to the Earth's surface, andregardless of whether or not they are within geographic region 220.

Wireless switching center 211 comprises a switch that orchestrates theprovisioning of telecommunications service to wireless terminal 201 andthe flow of information to and from location server 214, as describedbelow and in the accompanying figures. As is well known to those skilledin the art, wireless switching centers are also commonly referred to byother names such as mobile switching centers, mobile telephone switchingoffices, routers, etc.

Although the illustrative embodiment comprises one wireless switchingcenter, it will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention that comprise any number of wireless switching centers. Forexample, when a wireless terminal can interact with two or more wirelessswitching centers, the wireless switching centers can exchange and shareinformation that is useful in estimating the location of the wirelessterminal. For example, the wireless switching centers can use the IS-41protocol messages HandoffMeasurementRequest andHandoffMeasurementRequest2 to elicit signal-strength measurements fromone another. The use of two or more wireless switching centers isparticularly common when the geographic area serviced by the wirelessswitching center is small (e.g., local area networks, etc.) or whenmultiple wireless switching centers serve a common area.

In accordance with the illustrative embodiment, all of the base stationsservicing wireless terminal 201 are associated with wireless switchingcenter 211. It will be clear to those skilled in the art, after readingthis disclosure, how to make and use alternative embodiments of thepresent invention in which any number of base stations are associatedwith any number of wireless switching centers.

Assistance server 212 comprises hardware and software that is capable ofperforming the processes described below and in the accompanyingfigures. In general, assistance server 212 generates GPS assistance datafor wireless terminal 201 to aid wireless terminal 201 in acquiring andprocessing GPS ranging signals from GPS constellation 221. In accordancewith the illustrative embodiment, assistance server 212 is a separatephysical entity from location server 214; however, it will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention in which assistanceserver 212 and location server 214 share hardware, software, or both.

Location client 213 comprises hardware and software that use theestimate of the location of wireless terminal 201—provided by locationserver 214—in a location-based application, as described below and inthe accompanying figures.

Location server 214 comprises hardware and software that generate one ormore estimates of the location of wireless terminal 201 as describedbelow and in the accompanying figures. It will be clear to those skilledin the art, after reading this disclosure, how to make and use locationserver 214. Furthermore, although location server 214 is depicted inFIG. 2 as physically distinct from wireless switching center 211, itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which location server 214 is wholly or partially integratedwith wireless switching center 211.

In accordance with the illustrative embodiment, location server 214communicates with wireless switching center 211, assistance server 212,and location client 213 via a local area network; however it will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention in whichlocation server 214 communicates with one or more of these entities viaa different network such as, for example, the Internet, the PublicSwitched Telephone Network (PSTN), etc.

In accordance with the illustrative embodiment, wireless switchingcenter 211, assistance server 212, location client 213, and locationserver 214 are outside of geographic region 220. It will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention in which some orall of wireless switching center 211, assistance server 212, locationclient 213, and location server 214 are instead within geographic region220.

Location Server 214—FIG. 3 depicts a block diagram of the salientcomponents of location server 214 in accordance with the illustrativeembodiment. Location server 214 comprises: processor 301, memory 302,and local-area network transceiver 303, which are interconnected asshown.

Processor 301 is a general-purpose processor that is capable ofexecuting operating system 311 and application software 312, and ofpopulating, amending, using, and managing Location-Trait Database 313and Trait-Correction Database 314, as described in detail below and inthe accompanying figures. It will be clear to those skilled in the arthow to make and use processor 301.

Memory 302 is a non-volatile memory that stores:

-   -   i. operating system 311, and    -   ii. application software 312, and    -   iii. Location-Trait Database 313, and    -   iv. Trait-Correction Database 314.        It will be clear to those skilled in the art how to make and use        memory 302.

Transceiver 303 enables location server 214 to transmit and receiveinformation to and from wireless switching center 211, assistance server212, and location client 213. In addition, transceiver 303 enableslocation server 214 to transmit information to and receive informationfrom wireless terminal 201 and base stations 202-1 through 202-3 viawireless switching center 211. It will be clear to those skilled in theart how to make and use transceiver 303.

Operation of the Illustrative Embodiment

FIG. 4 depicts a flowchart of the salient processes performed inaccordance with the illustrative embodiment of the present invention.

In accordance with process 401, Location-Trait Database 313 is built.For the purposes of this specification, the “Location-Trait Database” isdefined as a database that maps each of a plurality of locations to oneor more expected traits associated with a wireless terminal at thatlocation. The details of building Location-Trait Database 313 aredescribed below and in the accompanying figures.

In accordance with process 402, Trait-Correction Database 314 is built.For the purposes of this specification, the “Trait-Correction Database”is defined as a database that indicates how the measurement of traitscan be adjusted to compensate for systemic measurement errors. Thedetails of building Trait-Correction Database 314 are described belowand in the accompanying figures.

In accordance with process 403, the location of wireless terminal 201 isestimated based on location-trait database 401, trait-correctiondatabase 402, and a variety of traits that vary based on the location ofwireless terminal 201. The details of process 403 are described belowand in the accompanying figures.

In accordance with process 404, the estimate of the location of wirelessterminal 201 is used in a location-based application, such as andwithout limitation, E 9-1-1 service. The details of process 404 aredescribed below and in the accompanying figures.

In accordance with process 405, Location-Trait Database 313 andTrait-Correction Database 314 are maintained so that their contents areaccurate, up-to-date and complete. Process 405 is advantageous becausethe effectiveness of the illustrative embodiment is based on—and limitedby—the accuracy, freshness, and completeness of the contents ofLocation-Trait Database 313 and Trait-Correction Database 314. Thedetails of process 405 are described below and in the accompanyingfigures.

Building Location-Trait Database 313—FIG. 5 depicts a flowchart of thesalient processes performed in accordance with process 401—buildingLocation-Trait Database 313.

In accordance with process 501, geographic region 220 is partitionedinto B(T,N) locations, wherein B(T,N) is a positive integer greater thanone, and wherein B(T,N) varies as a function of calendrical time T andthe environmental conditions N. It will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the number of locationsthat geographic region 220 is partitioned into is static. Furthermore,it will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the number of locations that geographic region 220 ispartitioned into is not dependent on the calendrical time T or theenvironmental conditions N.

Some traits of the radio frequency spectrum and of individual signalsare different at different locations in geographic region 220.Similarly, some traits of the radio frequency spectrum and of individualsignals transmitted by wireless terminal 201 change at base stations202-1, 202-2, and 202-3 when wireless terminal 201 is at differentlocations. Furthermore, some traits (e.g., hand-off state, etc.) ofwireless telecommunications system 200 change when wireless terminal 201is at different locations.

When wireless terminal 201 is at a particular location, the values ofthe traits that vary with the location of wireless terminal 201represent a “fingerprint” or “signature” for that location that enableslocation server 214 to estimate the location of wireless terminal 201.For example, suppose that under normal conditions the traits have afirst set of values when wireless terminal 201 is at a first location,and a second set of values when wireless terminal 201 is at a secondlocation. Then when wireless terminal 201 is at an unknown location andthe traits at that unknown location match the second set of values, itis more likely that wireless terminal 201 is at the second location.

Although human fingerprints and handwritten signatures are generallyconsidered to be absolutely unique, the combination of traits associatedwith each location might not be absolutely unique in geographic region220. The effectiveness of the illustrative embodiment is enhanced,however, as differences in the values of the traits among the locationsincreases. It will be clear to those skilled in the art, after readingthis disclosure, how to select locations and traits in order to increasethe likelihood that the values of the traits associated with eachlocation are distinguishable from the values of the traits associatedwith the other locations.

Each location is described by:

-   -   i. a unique identifier b,    -   ii. its dimensionality (e.g., one-dimension, two dimensions,        three dimensions, four-dimensions, etc.),    -   iii. the coordinates (e.g., latitude, longitude, altitude, etc.)        that define its scope (e.g., position, area, volume, etc.),        which can be static or, alternatively, can vary as a function of        calendrical time T or the environmental conditions N, or both        the calendrical time T and the environmental conditions N.    -   iv. the expected value E(b, T, N, W, Q) for each trait, Q, when        wireless terminal W is at location b at calendrical time T given        environmental conditions, N,    -   v. the identities of its adjacent locations, and    -   vi. the staying and moving probabilities P_(S)(b, T, N, W) and        P_(M)(b, T, N, W, c).

In accordance with the illustrative embodiment, the identifier of eachlocation is an arbitrarily-chosen positive integer. It will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention in which theidentifier of some or all locations is not arbitrarily chosen.Furthermore, it will be clear to those skilled in the art, after readingthis disclosure, how to make and use alternative embodiments of thepresent invention in which the identifier of some or all locations isnot a positive integer.

In accordance with the illustrative embodiment, the scope of eachlocation is three-dimensional and is described by (i) one or morethree-dimensional coordinates and geometric identifiers that define itsboundaries, (ii) a three-dimensional coordinate that resides at thecentroid of the location, and (iii) a description of how the scopechanges as a function of calendrical time T and environmental conditionsN. It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the scope of some or all of the locations areone-dimensional or two-dimensional. Furthermore, it will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention in which the scopeof some or all of the locations are not a function of calendrical time Tor environmental conditions N.

In accordance with the illustrative embodiment, the scope of two or morelocations can overlap at zero, one, two, more than two, or all points oflatitude and longitude (e.g., an overpass and underpass, differentstories in a multi-story building as described below, etc.).

In accordance with the illustrative embodiment, the boundaries of eachlocation are based, at least in part, on:

-   -   i. natural and man-made physical attributes of geographic region        220 (e.g., buildings, sidewalks, roads, tunnels, bridges, hills,        walls, water, cliffs, rivers, etc.),    -   ii. legal laws governing geographic region 220 (e.g., laws that        pertain to the location and movement of people and vehicles,        etc.),    -   iii. theoretical predictions and empirical data regarding the        location and movement of individuals and groups of people and        vehicles in geographic region 220,    -   iv. the desired accuracy of the estimates made by location        server 214, and    -   v. patterns of the location and movement of people and vehicles        within geographic region 220,    -   vi. the calendrical time T, and    -   vii. the environmental conditions N,        subject to the following considerations:

First, the accuracy with which wireless terminal 201 can be locatedpotentially increases with smaller location sizes. Not all locationsneed to be the same size, however, and areas requiring greater accuracycan be partitioned into smaller sizes, whereas areas requiring lessaccuracy can be partitioned into larger sizes.

Second, as the number of locations in geographic region 220 increases,so does the computational burden on location server 214 as describedbelow with respect to FIG. 10.

Third, as the size of adjacent locations decreases, the likelihoodincreases that the expected values for the traits in those locationswill be identical or very similar, which can hinder the ability oflocation server 214 to correctly determine when wireless terminal 201 isin one location versus the other.

With these considerations in mind, it will be clear to those skilled inthe art, after reading this disclosure, how to make and use alternativeembodiments of the present invention that partition geographic region220 into any number of locations of any size, shape, and arrangement.Furthermore, it will be clear to those skilled in the art, after readingthis disclosure, how to make and use embodiments of the presentinvention in which the locations are identical in size and shape.

FIG. 6 a depicts an isometric drawing of geographic region 220 and FIG.6 b depicts a map of geographic region 220. Geographic region 220comprises water fountain 601, park 602, four-story building 603,two-story building 604, various streets, sidewalks, and other featuresthat are partitioned into 28 locations as described below and depictedin FIGS. 6 c through 6 e. Although geographic region 220 comprisesapproximately four square blocks in the illustrative embodiment, it willbe clear to those skilled in the art how to make and use alternativeembodiments of the present invention with geographic regions of anysize, topology, and complexity.

In accordance with the illustrative embodiment, the eight roadintersections are partitioned into Locations 1 through 8, as depicted inFIG. 6 c. In accordance with the illustrative embodiment, the streetsections and their adjacent sidewalks up to the edge of buildings 603and 604 are partitioned into Locations 9 through 19, as depicted in FIG.6 d. In accordance with the illustrative embodiment, water fountain 601is partitioned into Location 20, park 602 is partitioned into Location25, each floor of building 604 is classified as one of Locations 21, 22,23, and 24, and each floor of building 603 is classified as of one ofLocations 27 and 28. It will be clear to those skilled in the art,however, after reading this disclosure, how to partition geographicregion 220 into any number of locations of any size and shape.

In accordance with an alternative embodiment of the present invention, ageographic region that comprises a clover-leaf intersection of two,four-lane divided highways is partitioned into 51 locations. FIG. 6 fdepicts an isometric drawing of the intersection, and FIG. 6 g depicts amap of the intersection. In accordance with the illustrative embodiment,the grass and medians have been partitioned into 15 locations asdepicted in FIG. 6 g, the four ramps have been partitioned into fourlocations as depicted in FIG. 6 h, the inner or “passing” lanes havebeen partitioned into eight locations as depicted in FIG. 6 i, and theouter or “travel” lanes have been partitioned into eight locations asdepicted in FIG. 6 j.

FIG. 6L depicts an alternative partitioning of geographic region 220into 64 square locations.

In accordance with process 502, the expected values E(b, T, N, W, Q) forthe following traits is associated with each location:

-   -   i. the expected pathloss of all of the signals receivable by        wireless terminal 201 when wireless terminal 201 is at the        location, from all transmitters (e.g., base stations 202-1,        202-2, and 202-3, commercial television, commercial radio,        navigation, ground-based aviation, etc.), as a function of the        calendrical time, T, and the environmental conditions, N; and    -   ii. the expected pathloss of all of the signals transmitted by        wireless terminal 201 when wireless terminal 201 is in the        location as receivable at base stations 202-1, 202-2, and 202-3,        as a function of the calendrical time, T, and the environmental        conditions, N; and    -   iii. the expected received signal strength of all of the signals        receivable by wireless terminal 201 when wireless terminal 201        is in the location, from all transmitters, as a function of the        calendrical time, T, and the environmental conditions, N; and    -   iv. the expected received signal strength of all of the signals        transmitted by wireless terminal 201 when wireless terminal 201        is in the location as receivable at base stations 202-1, 202-2,        and 202-3, as a function of the calendrical time, T, and the        environmental conditions, N; and    -   v. the expected received signal-to-impairment ratio (e.g.,        Eb/No, etc.) of all of the signals receivable by wireless        terminal 201 when wireless terminal 201 is in the location, from        all transmitters, as a function of the calendrical time, T, and        the environmental conditions, N; and    -   vi. the expected received signal-to-impairment ratio of all of        the signals transmitted by wireless terminal 201 when wireless        terminal 201 is in the location as receivable at base stations        202-1, 202-2, and 202-3, as a function of the calendrical time,        T, and the environmental conditions, N; and    -   vii. the expected received temporal difference of each pair of        multipath components (e.g., one temporal difference for one pair        of multipath components, a pair of temporal differences for a        triplet of multipath components, etc.) of all of the signals        receivable by wireless terminal 201 when wireless terminal 201        is in the location, from all transmitters, as a function of the        calendrical time, T, and the environmental conditions, N; and    -   viii. the expected received temporal difference of each pair of        multipath components (e.g., one temporal difference for one pair        of multipath components, a pair of temporal differences for a        triplet of multipath components, etc.) of all of the signals        transmitted by wireless terminal 201 when wireless terminal 201        is in the location as receivable at base stations 202-1, 202-2,        and 202-3, as a function of the calendrical time, T, and the        environmental conditions, N; and    -   ix. the expected received delay spread (e.g., RMS delay spread,        excess delay spread, mean excess delay spread, etc.) of all of        the signals receivable by wireless terminal 201 when wireless        terminal 201 is in the location, from all transmitters, as a        function of the calendrical time, T, and the environmental        conditions, N; and    -   x. the expected received delay spread (e.g., RMS delay spread,        excess delay spread, mean excess delay spread, etc.) of all of        the signals transmitted by wireless terminal 201 when wireless        terminal 201 is in the location as receivable at base stations        202-1, 202-2, and 202-3, as a function of the calendrical time,        T, and the environmental conditions, N; and    -   xi. the expected received relative arrival times of two or more        multipath components of all of the signals receivable by        wireless terminal 201 when wireless terminal 201 is in the        location, from all transmitters (which can be determined by a        rake receiver in well-known fashion), as a function of the        calendrical time, T, and the environmental conditions, N; and    -   xii. the expected received relative arrival times of two or more        multipath components of all of the signals transmitted by        wireless terminal 201 when wireless terminal 201 is in the        location as receivable at base stations 202-1, 202-2, and 202-3,        as a function of the calendrical time, T, and the environmental        conditions, N; and    -   xiii. the expected round-trip time of all of the signals        transmitted and receivable by wireless terminal 201 through base        stations 202-1, 202-2, and 202-3, as a function of the        calendrical time, T, and the environmental conditions, N; and    -   xiv. the expected round-trip time of all of the signals        transmitted and receivable by base stations 202-1, 202-2, and        202-3 through wireless terminal 201, as a function of the        calendrical time, T, and the environmental conditions, N; and    -   xv. the identity of the base stations that provide        telecommunications service to the location, as a function of the        calendrical time, T, and the environmental conditions, N; and    -   xvi. the identities of the neighboring base stations that        provide telecommunications service to the location, as a        function of the calendrical time, T, and the environmental        conditions, N; and    -   xvii. the handover state (e.g., soft, softer, 1×, 2×, etc.) of        wireless terminal 201 and wireless telecommunication system 200        when wireless terminal 201 is in the location as a function of        the calendrical time, T, and the environmental conditions, N.

In accordance with the illustrative embodiment of the present invention,all signals transmitted by wireless terminal 201 are for communicatingwith base stations 202-1 through 202-3, and all of the signals receivedby wireless terminal 201 are:

-   -   signals transmitted by base stations 202-1 through 202-3 for        communicating with wireless terminal 201,    -   television signals,    -   radio signals,    -   aviation signals, and    -   navigation signals.        It will be clear to those skilled in the art, after reading this        disclosure, how to make and use alternative embodiments of the        present invention that use different signals.

In accordance with the illustrative embodiment, the expected values ofthese traits are determined through a combination of:

-   -   i. a plurality of theoretical and empirical radio-frequency        propagation models, and    -   ii. a plurality of empirical measurements of the traits within        geographic region 220, in well-known fashion. The empirical        measurements of the traits are stored within location-trait        database 313 and updated as described below.

In accordance with the illustrative embodiment of the present invention,each location b is described by the identities of its adjacentlocations, (i.e., the locations that wireless terminal 201 canreasonably move into from location b within one time step Δt.) Inaccordance with the illustrative embodiment, two locations areconsidered to be “adjacent” when and only when they have at least twopoints in common. It will be clear to those skilled in the art, however,after reading this disclosure, how to make and use alternativeembodiments of the present invention in which two locations areconsidered adjacent when they have zero points or one point in common.

Adjacency Graph—In accordance with the illustrative embodiment, a datastructure is created that indicates which locations are adjacent. Thisdata structure is called an “adjacency graph” and it is stored withinLocation-Trait Database 313 in sparse-matrix format. FIG. 6 m depicts agraphical representation of the adjacency graph for the 28 locationsthat compose geographic area 220, and FIG. 6 n depicts a graphicalrepresentation of the adjacency graph for the 51 locations that composethe highway intersection in FIGS. 6 f through 6 k.

As described in detail below and in the accompanying figures, theadjacency graph is used in the temporal analysis of wireless terminal201's movements. It will be clear to those skilled in the art, afterreading this disclosure, how to make the adjacency graph for anypartitioning of geographic region 220.

In accordance with the illustrative embodiment, the staying and movingprobabilities P_(S)(b, T, N, W) and P_(M)(b, T, N, W, c) for all b aregenerated based on a model of the movement of wireless terminal W thatconsiders:

-   -   i. the topology of the adjacency graph; and    -   ii. the calendrical time T; and    -   iii. the environmental conditions N; and    -   iv. the natural and man-made physical attributes that affect the        location and movement of wireless terminals and the entities        that carry them (e.g., buildings, sidewalks, roads, tunnels,        bridges, hills, walls, water, cliffs, rivers, etc.); and    -   v. the legal laws governing the location and movement of        wireless terminals and the entities that carry them (e.g.,        one-way streets, etc.); and    -   vi. the past data for the movement of all wireless terminals;        and    -   vii. the past data for the movement of wireless terminal W.        It will be clear to those skilled in the art, after reading this        disclosure, how to make and use alternative embodiments of the        present invention that use any subcombination of i, ii, iii, iv,        v, vi, and vii to generate the staying and moving probabilities        for each location b.

The moving probabilities P_(M)(b, T, N, W, c) associated with a locationb can be considered to be either isotropic or non-isotropic. For thepurposes of this specification, “isotropic moving probabilities” aredefined as those which reflect a uniform likelihood of direction ofmovement and “non-isotropic moving probabilities” are defined as thosewhich reflect a non-uniform likelihood of direction of movement. Forexample, for locations arranged in a two-dimensional regular hexagonalgrid the values of P_(M)(b, T, N, W, c) of location b are isotropic ifand only if they are all equal (e.g., P_(M)(b, T, N, W, c)=⅙ for eachadjacent location c). Conversely, the values of P_(M)(b, T, N, W, c) arenon-isotropic if there are at least two probabilities with differentvalues. As another example, for locations arranged in a two-dimensional“checkerboard” grid, the values of P_(M)(b, T, N, W, c) are isotropic ifand only if:

-   -   (i) the north, south, east, and west moving probabilities out of        location b all equal p,    -   (ii) the northeast, northwest, southeast, and southwest moving        probabilities out of location b all equal p/√{square root over        (2)}, and    -   (iii) 4p(1+1/√{square root over (2)})+P_(S)(b, T, N, W)=1.

Isotropic moving probabilities are simple to generate, but areconsiderably less accurate than non-isotropic moving probabilities thatare generated in consideration of the above criteria. Therefore, inaccordance with the illustrative embodiment, the moving probabilitiesare non-isotropic, but it will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention that use isotropic movingprobabilities.

Populating Trait-Correction Database 313—FIG. 7 depicts a flowchart ofthe salient processes performed as part of process 402: populatingTrait-Correction Database 313.

In general, the ability of location server 214 to estimate the locationof wireless terminal 201 is limited by the accuracy with which thetraits are measured by wireless terminal 201 and by base stations 202-1,202-2, and 202-3. When the nature or magnitude of the measurement errorsis unpredictably inaccurate, there is little that can be done toovercome them.

In contrast, when the nature and magnitude of the measurement errors arepredictable, they can be corrected, and the nature and magnitude of somemeasurement errors are, in fact, predictable. For example, one make andmodel of wireless terminal is known to erroneously measure and reportthe signal strength of signals by −2 dB. If the measurements from thismodel of wireless terminal are left uncorrected, this −2 dB error couldcause location server 214 to erroneously estimate the location of thewireless terminal. In contrast, if location server 214 adds 2 dB to themeasurements from that make and model of wireless terminal, thelikelihood that location server 214 would erroneously estimate thelocation of the wireless terminal would be reduced.

Trait-Correction Database 313 comprises the information needed bylocation server 214 to be aware of systemic measurement errors and tocorrect them. A technique for eliminating some situational errors in themeasurements is described below and in the accompanying figures.

In accordance with process 701, a distortion function is generated forevery radio that might provide measurements to location server 214 andfor every trait whose measurements can be erroneous.

In general, the distortion function D(A,K,Q) relates the reportedmeasurement R for a trait Q to the actual value A for that trait and thedefining characteristic K of the radio making the measurement:R=D(A,K,Q).  (Eq. 1)

In accordance with the illustrative embodiment, the distortion functionD(A,K,Q) is provided to the owner/operator of location server 214 by theradio manufacturer. It will be clear to those skilled in the art,however, after reading this disclosure, how to generate the distortionfunction D(A,K,Q) for any radio without the assistance of the radiomanufacturer.

An ideal radio perfectly measures and reports the value of the traits itreceives and the distortion function D(A,K,Q) for one trait and for anideal radio is depicted in FIG. 8 a. As can be seen from the graph inFIG. 8 a, the salient characteristic of an ideal radio is that thereported value of the measurement, R, is exactly equal to the actualvalue of the trait A at the radio (i.e., there is no measurement orreporting error).

In contrast, most real-world radios do not perfectly measure the traitsof the signals they receive. This is particularly true for measurementsof signal-strength where the errors can be large. For example, FIG. 8 bdepicts a graph of the distortion function of an illustrative real-worldradio. In this case, the reported measurement is too high for somevalues, too low for others, and correct for only one value.

The nature and magnitude of each of the errors in the reportedmeasurements is inherent in the distortion function D(A,K,Q), and,therefore, knowledge of the distortion function enables the measurementerrors to be compensated for. In other words, when location server 214knows exactly how a radio distorts a measurement, it can correct—orcalibrate—the reported measurement with a calibration function to derivethe actual value of the trait. The calibration function, denotedC(R,K,Q), is generated in process 1102.

In accordance with the illustrative embodiment, the distortion functionD(A,K,Q) for all measurements is represented in tabular form. Forexample, the distortion function for one type of signal-strengthmeasurement for various radios is shown in Table 1. It will be clear tothose skilled in the art, after reading this disclosure, however, how tomake and use alternative embodiments of the present invention in whichthe distortion function for some or all measurements is not representedin tabular form. Furthermore, it will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention that comprise distortion functionsfor any type of measurement of any type of trait and for any radio.

TABLE 1 The Distortion function D(A, K, Q) in Tabular Form R = D(A, K,Q) K = Motorola K = Samsung Model A008; Q = Model A800; Q = A SignalStrength . . . Signal Strength −110 −115 . . . −107 −109 −114 . . . −106. . . . . . . . . . . .  −48  −38 . . .  −50  −47  −37 . . .  −49

The purpose of the characteristic, K, is to identify which calibrationfunction should be used in calibrating the reported measurements fromwireless terminal 201, and, therefore, the characteristic, K, should beas indicative of the actual distortion function for wireless terminal201 as is economically reasonable.

For example, the characteristic, K, can be, but is not limited to:

-   -   i. the unique identity of wireless terminal 201 (e.g., its        electronic serial number (“ESN”), its international mobile        station identifier (“IMSI”), its temporary international mobile        station identifier (“TIMSI”), mobile station identification        (“MSID”), its directory number (“DN”), etc.); or    -   ii. the model of wireless terminal 201 (e.g., Timeport 210 c,        etc.); or    -   iii. the make (i.e., manufacturer) of wireless terminal 201        (e.g., Motorola, Samsung, Nokia, etc.); or    -   iv. the identity of the radio-frequency circuitry of wireless        terminal 201 (e.g., Motorola RF circuit design 465B, etc.); or    -   v. the identity of one or more components of wireless terminal        201 (e.g., the part number of the antenna, the part number of        the measuring component, etc.); or    -   viii. any combination of i, ii, iii, iv, v, vi, and vii.

The most accurate characteristic is the unique identity of wirelessterminal 201 because that would enable location server 214 to use thecalibration function generated for that very wireless terminal. It isunlikely, however, that this is economically feasible because it wouldrequire that every wireless terminal be tested to determine its ownunique distortion function.

On the other hand, using only the make of wireless terminal 201 as thecharacteristic, K, is economically reasonable, but it is unlikely that asingle calibration function for all of a manufacturer's wirelessterminals would provide very accurate calibrated signal-strengthmeasurements.

As a compromise, the illustrative embodiment uses the combination ofmake and model of wireless terminal 201 as the characteristic, K,because it is believed that the amount of variation between wirelessterminals of the same make and model will be small enough that a singlecalibration function for that model should provide acceptably accuratecalibrated measurements for every wireless terminal of that make andmodel.

It will be clear to those skilled in the art, however, after readingthis disclosure, how to make and use alternative embodiments of thepresent invention in which the characteristic, K, is based on somethingelse.

In accordance with process 502, the calibration function C(R,K,Q) isgenerated for every radio that might provide measurements to locationserver 214 and for every trait whose measurements can be distorted.

In general, the calibration function C(R,K,Q) relates the calibratedmeasurement S of a trait Q, to the reported measurement R of trait Q andthe defining characteristic K of the radio making the measurement:S=D(R,K,Q)  (Eq. 2)

The calibration function C(R,K,Q) is the inverse of the distortionfunction D(A,K,Q). In other words, the salient characteristic of thecalibration function C(R,K,Q) is that it satisfies the equation 3:S=A=C(D(A,K,Q),K,Q)  (Eq. 3)so that the calibrated measurement, S, is what the reported measurement,R, would have been had the radio making and reporting the measurementbeen ideal. It will be clear to those skilled in the art, after readingthis disclosure, how to derive C(R,K,Q) from D(A,K,Q). FIG. 8 c depictsa graph of the calibration function C(R,K,Q) for the distortion functionD(A,K,Q) depicted in FIG. 8 b.

In accordance with the illustrative embodiment, the function C(R,K,Q) isrepresented in tabular form, such as that shown in Table 2.

TABLE 2 The Calibration Function C(R, C, N) in Tabular Form S = C(R, C,N) C = Motorola C = Samsung Model A008; Q = Model A800; Q = R SignalStrength . . . Signal Strength −110 −115 . . . −107 −109 −114 . . . −106. . . . . . . . . . . .  −48  −38 . . .  −50  −47  −37 . . .  −49

In accordance with process 402, the calibration functions C(R,K,Q) arestored in Trait-Corrections Database 313.

Maintaining Location-Trait Database 313—FIG. 9 depicts a flowchart ofthe salient processes performed in process 403: maintainingLocation-Trait Database 313 and Trait-Corrections Database 314. Theability of the illustrative embodiment to function is based on—andlimited by—the accuracy, freshness, and completeness of the informationcontained in Location-Trait Database 313 and Trait-Corrections Database314.

In accordance with process 901, a drive-test regimen is developed thatperiodically makes empirical measurements throughout geographic region220 with highly-accurate equipment to ensure the accuracy, freshness,and completeness of the information contained in Location-Trait Database313 and Trait-Corrections Database 314.

In accordance with process 902, the drive-test regimen is implemented.

In accordance with process 903, Location-Trait Database 313 andTrait-Corrections Database 314 are updated, as necessary.

Estimating the Location of Wireless Terminal 201—FIG. 10 depicts aflowchart of the salient processes performed in process 403: estimatingthe location of wireless terminal 201. In accordance with theillustrative embodiment, process 403 is initiated by a request fromlocation client 213 for the location of wireless terminal 201. It willbe clear to those skilled in the art, however, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which process 403 is initiated periodically, sporadically,or in response to some other event.

In accordance with process 1001, Y probability distributions for thelocation of wireless terminal 201 are generated for each of instants H₁through H_(Y) in the temporal interval ΔT, wherein Y is a positiveinteger, based on comparing the measurements of traits associated withwireless terminal 201 at each of instants H₁ through H_(Y) to expectedvalues for those traits at those times. Each of the Y probabilitydistributions provides a first estimate of the probability that wirelessterminal 201 is in each location at each of instants H₁ through H_(Y).The details of process 1001 are described below and in the accompanyingfigures.

In accordance with process 1002, Z probability distributions for thelocation of wireless terminal 201 are generated for each of instants A₁though A_(Z) in the temporal interval ΔT, wherein Z is a positiveinteger, based on Assisted GPS measurements at wireless terminal 201 ateach of instants A₁ though A_(Z). Each of the Z probabilitydistributions provides a first estimate of the probability that wirelessterminal 201 is in each location at each of instants A₁ though A_(Z).The details of process 1002 are described below and in the accompanyingfigures.

In accordance with process 1003, the Y probability distributionsgenerated in process 1001 and the Z probability distributions generatedin process 1002 are combined, taking into account their temporal order,to generate a second estimate of the location of wireless terminal 201.The details of process 1003 are described below and in the accompanyingfigures.

Generating the Probability Distributions for the Location of WirelessTerminal 201 Based on Pattern Matching of Traits—FIG. 11 a depicts aflowchart of the salient processes performed in process 1001—generatingthe Y probability distributions for the location of wireless terminal201 based on comparing the measurements of traits associated withwireless terminal 201 at each of instants H₁ through H_(Y) to expectedvalues for those traits at those times. In accordance with theillustrative embodiment, location server 214 performs each of processes1101 through 1105 as soon as the data necessary for performing theprocess becomes available to it.

In accordance with process 1101, location server 214 receives Ynon-empty sets of measurements of the traits, M₁ though M_(Y),associated with wireless terminal 201. Each set of measurements is madeat one of instants H₁ through H_(Y).

In accordance with the illustrative embodiment, each set of measurementscomprises:

-   -   i. the pathloss of all of the signals received by wireless        terminal 201 from all transmitters (e.g., base stations 202-1,        202-2, and 202-3, commercial television, commercial radio,        navigation, ground-based aviation, etc.); and    -   ii. the pathloss of all of the signals transmitted by wireless        terminal 201 as received at base stations 202-1, 202-2, and        202-3; and    -   iii. the received signal strength of all of the signals received        by wireless terminal 201 from all transmitters; and    -   iv. the received signal strength of all of the signals        transmitted by wireless terminal 201 as received at base        stations 202-1, 202-2, and 202-3; and    -   v. the received signal-to-impairment ratio of all of the signals        received by wireless terminal 201 from all transmitters; and    -   vi. the received signal-to-impairment ratio of all of the        signals transmitted by wireless terminal 201 as received at base        stations 202-1, 202-2, and 202-3; and    -   vii. the received temporal difference of each pair of multipath        components of all of the signals received by wireless terminal        201 from all transmitters; and    -   viii. the received temporal difference of each pair of multipath        components of all of the signals transmitted by wireless        terminal 201 as received at base stations 202-1, 202-2, and        202-3; and    -   ix. the received delay spread of all of the signals received by        wireless terminal 201 from all transmitters; and    -   x. the received delay spread of all of the signals transmitted        by wireless terminal 201 as received at base stations 202-1,        202-2, and 202-3; and    -   xi. the received relative arrival times of two or more multipath        components of all of the signals received by wireless terminal        201 from all transmitters; and    -   xii. the received relative arrival times of two or more        multipath components of all of the signals transmitted by        wireless terminal 201 as received at base stations 202-1, 202-2,        and 202-3; and    -   xiii. the round-trip time of all of the signals transmitted and        received by wireless terminal 201 through base stations 202-1,        202-2, and 202-3; and    -   xiv. the round-trip time of all of the signals transmitted as        received at base stations 202-1, 202-2, and 202-3 through        wireless terminal 201; and    -   xv. the identity of the base stations that provide        telecommunications service to wireless terminal 201; and    -   xvi. the identities of the neighboring base stations that can        provide telecommunications service to wireless terminal 201; and    -   xvii. the handover state (e.g., soft, softer, 1×, 2×, etc.) of        wireless terminal 201 and wireless telecommunication system 200;        and    -   xviii. an indication of the calendrical time, T; and    -   xix. an indication of the environmental conditions, N.

In accordance with the illustrative embodiment, wireless terminal 201provides its measurements directly to location server 214 via the userplane and in response to a request from location server 214 to do so.This is advantageous because the quality of the estimate of the locationof wireless terminal 201 is enhanced when there are no limitations onthe nature, number, or dynamic range of the measurements—as might occurwhen measurements are required to be made in accordance with theair-interface standard. It will be clear to those skilled in the art,however, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which wireless terminal 201provides its measurements periodically, sporadically, or in response tosome other event. Furthermore, it will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which wireless terminal 201provides its measurements to location server 214 via the UMTS protocol.

In accordance with the illustrative embodiment, base stations 202-1,202-2, and 202-3 provide their measurements to location server 214 viawireless switching center 211 and in response to a request from locationserver 214 to do so. It will be clear to those skilled in the art,however, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which base stations 202-1,202-2, and 202-3 provide their measurements to location server 214periodically, sporadically, or in response to some other event.

As part of process 1101, location server 214 also receives from wirelessterminal 201:

-   -   i. the identities of the base stations that provided service to        wireless terminal 201 at each of instants H₁ through H_(Y), and    -   ii. the identities of the neighboring base stations that        provided service to the location of wireless terminal 201 at        each of instants H₁ through H_(Y).        This information is used by location server 214 in performing        search area reduction, which is described in detail below.

In accordance with process 1102, location server 214 uses thecalibration functions C(R,K,Q) in the Trait-Corrections Database 314 tocorrect the systemic errors in the measurements received in process1001.

In accordance with process 1103, location server 214 computes thedifferentials, in those cases that are appropriate, of the measurementsto correct the situational errors in the measurements received inprocess 1001. Many factors, including the condition of wireless terminal201's antenna, the state of its battery, and whether or not the terminalis inside a vehicle can introduce situational measurement errors. Thisis particularly true for measurements of pathloss and signal strength.

The illustrative embodiment ameliorates the effects of these factors bypattern matching not the measurements themselves—whether corrected inprocess 1102 or not—to the expected values for those traits, but bypattern matching the pair-wise differentials of those measurements tothe pair-wise differentials of the expected values for those traits. Itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which different measurements are corrected for situationalerrors by the use of pair-wise differentials.

A simple example involving signal strengths illustrates this approach. Afirst radio station, Radio Station A, can be received at −56 dBm atLocation 1, −42 dBm at Location 2, −63 dBm at Location 3, and −61 dBm atLocation 4, and a second radio station, Radio Station B, can be receivedat −63 dBm at Location 1, −56 dBm at Location 2, −65 dBm at Location 3,and −52 dBm at Location 4. This information is summarized in the tablebelow and forms the basis for a map or database that correlates locationto signal strength.

TABLE 3 Illustrative Location-Trait Database (Differential Reception)Radio Radio Station A Station B Difference Location 1 −56 dBm −63 dBm −7dB Location 2 −42 dBm −56 dBm −14 dB  Location 3 −63 dBm −65 dBm −2 dBLocation 4 −61 dBm −52 dBm   9 dB

If a given wireless terminal with a broken antenna and at an unknownlocation receives Radio Station A at −47 dBm and Radio Station B at −61dBm, then it registers Radio Station A as 14 dBm stronger than RadioStation B. This suggests that the wireless terminal is more likely to beat Location 2 than it is at Location 1, 3, or 4. If the measured signalstrengths themselves were pattern matched into Location-Trait Database313, the resulting probability distribution for the location of wirelessterminal 201 might not be as accurate.

A disadvantage of this approach is that the situational bias iseliminated at the expense of (1) doubling the variance of the randommeasurement noise, and (b) reducing the number of data points to patternmatch by one. Furthermore, the pair-wise subtraction introducescorrelation into the relative signal strength measurement errors (i.e.,all of the data points to be matched are statistically correlated). Itwill be clear to those skilled in the art how to account for thiscorrelation in calculating the likelihood of the measurement report.

In accordance with process 1104, location server 214 performs atechnique called “search area reduction” in preparation for process1105. To understand what search area reduction is and why it isadvantageous, a brief discussion of process 1105 is helpful. In process1105 location server 214 estimates the probability that wirelessterminal 201 is in each location at each of instants H₁ through H_(Y).This requires generating Y multi-dimensional probability distributions,one for each of instants H₁ through H_(Y).

The process for generating each multi-dimensional probabilitydistribution can be computationally intensive and the intensity dependson the number of locations that must be considered as possible locationsfor wireless terminal 201. When the number of locations that must beconsidered is small, the process can be performed quickly enough formany “real-time” applications. In contrast, when the number of locationsthat must be considered is large, the process can often take too long.

Nominally, all of the locations in geographic region 220 must beconsidered because, prior to process 1104, wireless terminal 201 couldbe in any location. In accordance with the illustrative embodiment,geographic region 220 comprises only 28 locations. In many alternativeembodiments of the present invention, however, geographic region 220comprises thousands, millions, or billions of locations. Theconsideration of thousands, millions, or billions of locations for eachinstant by location server 214 might take too long for many real-timeapplications.

Therefore, to expedite the performance of process 1105, location server214 performs some computationally-efficient tests that quickly andsummarily eliminate many possible locations for wireless terminal 201from consideration, and, therefore, summarily set to zero theprobability that wireless terminal 201 is at those locations. Thisreduces the number of locations that must be fully considered in process1105 and generally improves the speed with which process 1001 isperformed.

In accordance with search area reduction, for each of instants Hathrough H_(Y) location server 214 uses six computationally efficienttests in an attempt to designate one or more locations as improbablelocations for wireless terminal 201. A location that is designated asimprobable by one or more of the six tests at instant H_(i) isdesignated as improbable by process 1104 at instant H_(i). To the extentthat a location is designated as improbable at instant H_(i), thecomputational burden on location server 214 of generating theprobability distribution for that instant is reduced.

There are two types of errors that can be made by process 1104. Thefirst type of error—a Type I error—occurs when process 1104 designates alocation as improbable when, in fact, it is not improbable for wirelessterminal 201 to be in that location. The second type of error—a Type IIerror—occurs when process 1104 fails to designate a location asimprobable when, in fact, it is improbable that wireless terminal 201 isin that location.

In general, a Type I error affects the accuracy with which theillustrative embodiment can estimate the location of wireless terminal201, and a Type II error affects the speed with which processor 1104 cangenerate the probability distributions. In accordance with theillustrative embodiment, the tests and their parameters are chosen tobalance the number of Type I and Type II errors with the computationalcomplexity and value of process 1104. For example, when there are toomany Type II errors, the value of process 1104 is undermined by thecomputational burden of process 1104. It will be clear those skilled inthe art, after reading this disclosure, how to make and use alternativeembodiments of the present invention that have any number of Type I andType II errors.

FIG. 11 b depicts a flowchart of the salient processes performed inaccordance with process 1104: search area reduction.

In accordance with process 1111, location server 214 designates alocation as improbable when the difference between a measured value of atrait and the expected value of that trait at that location exceeds athreshold. The theory underlying this test is that a major discrepancybetween a measurement of a trait and the expected value of a trait at alocation suggests that the measurement was not made when wirelessterminal 201 was in that location. In accordance with the illustrativeembodiment, location engine 214 performs process 1111 on each measuredvalue of each trait for each signal for each of instants H₁ throughH_(Y). It will be clear to those skilled in the art, after reading thisdisclosure, how to choose the traits and signals and thresholds toachieve the desired number of Type I and Type II errors. It will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention that omitprocess 1111 or that omit testing one or more traits and/or one or moresignals in process 1111.

In accordance with process 1112, when the magnitude of two measurementsof a trait at one instant exceed a first threshold and the magnitude ofthe expected values for that trait at a location exceed a secondthreshold, location server 214 designates that location as improbablewhen a ranking of the two measurements differs from a ranking of theexpected values. The theory underlying this test is that a majordiscrepancy between the ranking of the measurements of a trait and theranking of the expected values of that trait in the location suggeststhat the measurements were not made when wireless terminal 201 was inthat location. In accordance with the illustrative embodiment, locationengine 214 performs process 1112 on each pair of measurements of eachtrait for each of instants H₁ through H_(Y). It will be clear to thoseskilled in the art, after reading this disclosure, how to choose thetraits and signals and thresholds to achieve the desired number of TypeI and Type II errors. It will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention that omit process 1112 or that omittesting one or more traits and/or one or more signals in process 1112.

In accordance with process 1113, location server 214 designates alocation as improbable when a measurement of traits of a signal is notreceived when it is expected if wireless terminal 201 were, in fact, inthat location. In accordance with the illustrative embodiment, locationengine 214 performs process 1113 on each trait of each expected signalfor each of instants H₁ through H_(Y). This test is highly prone to TypeI errors and should be used judiciously. It will be clear to thoseskilled in the art, after reading this disclosure, how to make and usealternative embodiments of the present invention that omit process 1113or that omit testing one or more traits and/or one or more signals inprocess 1113.

In accordance with process 1114, location sever 214 designates alocation as improbable when a measurement of a trait of a signal isreceived when it is not expected if wireless terminal 201 were, in fact,in that location. In accordance with the illustrative embodiment,location engine 214 performs process 1114 on each trait of each signalfor each of instants H₁ through H_(Y). In general, this test is lessprone to Type I errors than the test in process 1113. It will be clearto those skilled in the art, after reading this disclosure, how to makeand use alternative embodiments of the present invention that omitprocess 1114 or that omit testing one or more traits and/or one or moresignals in process 1114.

In accordance with process 1115, location server 214 designates alocation as improbable when the location is not provided wirelesstelecommunications service by a base station that is known to beproviding service to wireless terminal 201 at that instant. The theoryunderlying this test is that if a base station that providedtelecommunications service to wireless terminal 201 at that instant doesnot provide service to the location, then it suggests that wirelessterminal 201 is not in that location at that instant. In general, thistest is highly accurate and has a low number of both Type I and Type IIerrors. It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention that omit process 1115.

In accordance with process 1116, location server 214 designates alocation as improbable designating a possible location as improbablewhen the location is not within the neighboring coverage area of a basestation that is known to be a neighboring base station of wirelessterminal 201. The theory underlying this test is that if a location isnot within the neighboring coverage area of a base station that is aneighbor of wireless terminal 201 at that instant, then it suggests thatwireless terminal 201 is not in the location at that instant. Ingeneral, this test is highly accurate and has a low number of both TypeI and Type II errors. It will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention that omit process 1116.

A location that that is designated as improbable at instant H_(i) by oneor more of processes 1111 through 1116 is designated as improbable byprocess 1104 at instant H_(i).

In accordance with process 1105, location server 214 generates each ofthe Y probability distribution for that wireless terminal 201 at each ofinstants H₁ through H_(Y). To accomplish this, location server 214performs the processes described below and in FIG. 11 c.

FIG. 11 c depicts a flowchart of the salient processes performed inaccordance with process 1105: generating the Y probability distributionfor that wireless terminal 201 at each of instants H₁ through H_(Y).

In accordance with process 1121, location server 214 sets theprobability of wireless terminal 201 being at a location at instantH_(i) to zero (0) if the location was designated as improbable atinstant H_(i) by process 1104.

In accordance with process 1122, location server 214 generates theEuclidean norm between the measurements of a trait and the expectedvalues for that trait at all instants and for all locations notdesignated as improbable by process 1104. To accomplish this, theEuclidean norm is generated between the measurements (as corrected inprocess 1102, if necessary and/or the differentials of measurements asthe case may be) of the expected values for those traits inLocation-Trait Database 313. To accomplish this, the Euclidean norm isgenerated as described in Equation 4:V(b,H _(i))=√{square root over (Σ((E(b,H _(i) ,N,W,Q)−M(b,H _(i),N,W,Q))·ω(Q))²)}{square root over (Σ((E(b,H _(i) ,N,W,Q)−M(b,H _(i),N,W,Q))·ω(Q))²)}{square root over (Σ((E(b,H _(i) ,N,W,Q)−M(b,H _(i),N,W,Q))·ω(Q))²)}  (Eq. 4)wherein V(b,H_(i)) is the Euclidean norm for Location b at instant H_(i)based on the square root of the sum of the square of the differencesbetween each (corrected and differential, where appropriate) traitmeasurement M(b, H_(i), N, W, Q) minus the expected value E(b, H_(i), N,W, Q) for that trait, where ω(Q) is a weighting factor that indicatesthe relative weight to be given discrepancies in one trait versusdiscrepancies in the other traits.

At accordance with process 1123, the un-normalized probabilities of thelocation of wireless terminal 201 at each location are generated basedon the Euclidean norms generated in process 1122 as shown in Equation 5.

$\begin{matrix}{{{UP}\left( {b,H_{i}} \right)} = {\mathbb{e}}^{(\frac{- {V^{2}{({b,H_{i}})}}}{\delta^{2}})}} & \left( {{Eq}.\mspace{14mu} 5} \right)\end{matrix}$wherein UP(b,H_(i)) represents the un-normalized probability thatwireless terminal 201 is in Location b at instant H_(i), and wherein δ²equals:

$\begin{matrix}{\delta^{2} = {\delta_{E}^{2} + \delta_{M}^{2}}} & \left( {{Eq}.\mspace{14mu} 6} \right)\end{matrix}$wherein δ_(E) ² is the square of the uncertainty in the error inLocation-Trait Database and δ_(M) ² is the square of the uncertainty inthe calibrated measurements. It will be clear to those skilled in theart, after reading this disclosure, how to generate δ².

At process 1124, the probabilities generated in process 1123 arenormalized as described in Equation 7.

$\begin{matrix}{{{NP}\left( {b,H_{i}} \right)} = \frac{{UP}\left( {b,H_{i}} \right)}{\sum{{UP}\left( {b,H_{i}} \right)}}} & \left( {{Eq}.\mspace{14mu} 7} \right)\end{matrix}$wherein NP(b,H_(i)) represents the normalized probability that wirelessterminal 201 is in Location b.

As part of process 1124, location server 214 generates a preliminaryestimate of the location of wireless terminal 201 at instant H₁ based onthe maximum likelihood function of the normalized probabilitydistribution at instant H_(i).

Generating the Probability Distributions for the Location of WirelessTerminal 201 Based on Assisted GPS—FIG. 12 depicts a flowchart of thesalient processes performed in process 1002: generating the Zprobability distributions for the location of wireless terminal 201based on GPS-derived information (i.e., information from GPSconstellation 221).

In accordance with processes 1124 and 1201, location server 214transmits, and assistance server 212 receives, the preliminary estimateof the location of wireless terminal 201 at instant H₁ as generated inprocess 1105.

In accordance with process 1202, assistance server 212 generatesassistance data for wireless terminal 201 based on the preliminaryestimate of the location of wireless terminal 201 at instant H₁. Inaccordance with the illustrative embodiment, assistance server 212generates “fully-custom” assistance data based on the estimate of thelocation of wireless terminal 201 at instant H₁. The assistance data is“fully-custom” because it is specifically tailored to the estimatedlocation of wireless terminal 201 at instant H₁. It will be clear tothose skilled in the art how to generate fully-custom assistance datafor wireless terminal 201 based on the estimated location of wirelessterminal 201 at instant H₁. As part of process 1202, assistance server212 transmits the assistance data to wireless terminal 201 via wirelessswitching center 212 in well-known fashion.

In accordance with some alternative embodiments of process 1202,assistance server 212 pre-computes assistance data for a plurality ofdiverse locations within geographic region 220 and selects thatpre-computed assistance data for wireless terminal 201 based on theestimated location of wireless terminal 201 at instant H₁. Because theassistance data selected for wireless terminal 201 is not specificallytailored to the estimated location of wireless terminal 201 at instantH₁, nor generic to all of geographic region 220 or to the cell or sectorof the base station serving wireless terminal 201, it is deemed“semi-custom” assistance data. In general, semi-custom assistance datais less accurate than fully-custom assistance data, but more accurate,on average, than generic assistance data, which is chosen based on cellID alone and that is based on one location within geographic region 220.It will be clear to those skilled in the art, after reading thisdisclosure, how to generate the fully-custom and semi-custom assistancedata for wireless terminal 201.

In accordance with process 1203, wireless terminal 201 (a) receives theassistance data from assistance server 212, in well-known fashion, (b)uses it to facilitate the acquisition and processing of one or more GPSsatellite signals in well-known fashion, and (c) transmits Z non-emptysets of GPS-derived information to location server 214 for readings atinstants G₁ through G_(Z), where Z is a positive integer. In accordancewith the illustrative embodiment of the present invention, each set ofGPS-derived information comprises:

-   -   i. a GPS-derived estimate of the location of wireless terminal        201 (e.g., a latitude, longitude, and altitude coordinate,        etc.), or    -   ii. ranging data (e.g., PRN code phase, etc.) from one or more        GPS satellites, or    -   iii. partially-processed ranging signals (e.g., signals from        which the ranging data has not yet been extracted, etc.) from        one or more GPS satellites, or    -   iv. any combination of i, ii, and iii.

In accordance with process 1204, location server 214 receives Znon-empty sets of GPS-derived information to location server 214 forreadings at instants G₁ through G_(Z) and generates a probabilitydistribution that indicates the likelihood that wireless terminal 201 isin each location at each of instants G₁ through G_(Z). It will be clearto those skilled in the art how to perform process 1204.

FIG. 13 depicts a flowchart of the salient processes performed inprocess 1003—combining the Y non-GPS-based probability distributionswith the Z GPS-based probability distributions to derive F refinedmulti-dimensional probability distributions for the location of wirelessterminal 201 at each of instants J₁ through J_(F), where each J_(i)corresponds to one of:

-   -   i. a particular instant H_(Y), where 1≦y≦Y, or    -   ii. a particular instant G_(Z), where 1≦z≦Z, or    -   iii. a concurrence of both a particular instant H_(Y), and a        particular instant G_(Z), where 1≦y≦Y and 1≦z≦Z.        In other words, each “composite” instant J_(i) corresponds to        either an instant associated with a non-GPS-based probability        distribution, or an instant associated with a GPS-based        probability distribution, or an instant associated with both a        non-GPS probability distribution and a GPS-based probability        distribution.

In accordance with process 1003, the Y non-GPS-based probabilitydistributions with the Z GPS-based probability distributions areintelligently combined, taking into consideration their relativetemporal occurrence to derive a refined multi-dimensional probabilitydistribution for the location of wireless terminal 201 at instants J₁through J_(F).

To generate the refined probability distribution for the location ofwireless terminal 201 at instant J_(i), the probability distributionsthat occur before instant J_(i) are temporally-extrapolatedprogressively to instant J_(i), the probability distributions that occurafter instant J_(i) are temporally-extrapolated regressively to instantJ_(i), and they all are combined with the un-temporally-extrapolatedprobability distribution for the location of wireless terminal 201 atinstant J_(i). In this way, the accuracy of all of the refinedprobability distributions for each instant J_(i) are enhanced by theempirical data at other instants.

FIG. 14 depicts a first example of determining each of instants J₁through J_(F) based on non-GPS-based instants H₁ through H_(Y), whereY=4, and GPS-based instants G₁ through G_(Z), where Z=6. As can be seenin FIG. 14, the number of composite instants F is at most Y plus Z, andis at least the maximum of Y and Z—the former occurring when there areno coincident GPS/non-GPS probability distributions, and the latter whenthere are as many as possible coincident GPS/non-GPS probabilitydistributions.

FIG. 15 depicts a second example of determining each of instants J₁through J_(F) based on non-GPS-based instants and GPS-based instants.This second example illustrates that even when the non-GPS-basedinstants are uniformly spaced in time and the GPS-based instants areuniformly spaced in time, the composite instants are not necessarilyuniformly spaced in time.

In accordance with the present invention, the time step Δt is defined asthe minimum time interval between any two instants. The time step isatomic in that the time difference between any two instants is anintegral multiple of time steps. (Note that two consecutiveinstants—whether they are non-GPS-based instants, GPS-based instants, orcomposite instants—might be more than a single time step apart.) Thetime step of the present invention is therefore similar to the time stepemployed in clock-driven discrete event simulations.

As will be appreciated by those skilled in the art, selecting anappropriate value for the time step Δt typically will depend on theparticular application, and involves a tradeoff between (1) temporalprecision and (2) available memory and processing power. As will befurther appreciated by those skilled in the art, after reading thisdisclosure, the selected time step can affect the definition oflocations, the moving and staying probabilities, and consequently thegraphs that are derived from them (e.g., the adjacency graph, etc.).

In accordance with process 1301, location server 214 determines instantsJ₁ through J_(F), as described above.

In accordance with process 1302, location server 214 constructsunrefined probability distributions V₁ through V_(F) for instants J₁through J_(F) as follows:

-   -   i. if J_(i) corresponds to a particular H_(j) only, then V_(i)        equals the non-GPS probability distribution at instant H_(j),    -   ii. if J_(i) corresponds to a particular G_(k) only, then V_(i)        equals the GPS probability distribution at instant G_(k), and    -   iii. otherwise (C_(i) corresponds to both a particular H_(j) and        a particular G_(k)), V_(i) equals a probability distribution        that equals the normalized product of the non-GPS and GPS        probability distributions at instant J_(i).

In accordance with process 1303, location server 214 determines for eachinstant J_(i), temporally-extrapolated probability distributions D_(i,j)for all j≠i, 1≦j≦F, which are based on (i) the unrefined probabilitydistribution V_(j) at instant J_(j), (ii) P_(S)(b, T, N, W), and (iii)P_(M)(b, T, N, W, c). The extrapolated probability distribution D_(i,j)is therefore a predictive probability distribution at instant J_(i) thatis based on empirical data at instant J_(j)—but not on any empiricaldata at other instants, including J_(i).

-   -   i. the past data for the movement of all wireless terminals; and    -   ii. the past data for the movement of wireless terminal W; and    -   iii. the location, speed, and acceleration of wireless terminal        W at calendrical time T; and    -   iv. the state of traffic signals that can affect the movement of        wireless terminals in location b.

A temporally-extrapolated probability distribution can be progressed(i.e., projected into the future based on a past probabilitydistribution). For example, if instant J₃ is one time step after instantJ₂, then extrapolated probability distribution D_(3,2) is derived by asingle application of P_(S)(b, T, N, W) and P_(M)(b, T, N, W, c) tounrefined probability distribution V₂. In other words, for any locationb:

$\begin{matrix}{{D_{3,2}\lbrack b\rbrack} = {{{V_{2}\lbrack b\rbrack} \cdot {P_{S}\left( {b,J_{2},N,W} \right)}} + {\sum\limits_{{{({c,b})} \in {i\;{n{(b)}}}}\;}{{V_{2}\lbrack c\rbrack} \cdot {P_{M}\left( {c,J_{2},N,W,b} \right)}}}}} & \left( {{Eq}.\mspace{14mu} 8} \right)\end{matrix}$where in(b) is the set of arcs into location b from other locations inthe adjacency graph. Similarly, a temporally-extrapolated probabilitydistribution can be regressed (i.e., projected into the past based on afuture unrefined probability distribution) based on the equation:

$\begin{matrix}{{V_{3}\lbrack b\rbrack} = {{{D_{2,3}\lbrack b\rbrack} \cdot {P_{S}\left( {b,J_{2},N,W} \right)}} + {\sum\limits_{{{({c,b})} \in {i\;{n{(b)}}}}\;}{{D_{2,3}\lbrack c\rbrack} \cdot {P_{M}\left( {c,J_{2},N,W,b} \right)}}}}} & \left( {{Eq}.\mspace{14mu} 9} \right)\end{matrix}$by setting up a system of equations (9) for a plurality of locations{b₁, b₂, . . . , b_(η)} and solving for {D_(2,3)[b₁], D_(2,3)[b₂], . . ., D_(2,3)[b_(η)]} via matrix algebra.

As will be well-understood by those skilled in the art, after readingthis disclosure, when consecutive instants are two or more time stepsapart, then Equation 8 can be applied iteratively in well-known fashion.(Because the time step is atomic the number of iterations is alwaysintegral.) As will be further appreciated by those skilled in the art,after reading this disclosure, the extrapolated probabilitydistributions for non-consecutive time instants (e.g., D_(2,4), D_(5,1),etc.) can be efficiently computed in a bottom-up fashion from theextrapolated probability distributions for consecutive time instants viadynamic programming.

In accordance with process 1304, location server 214 computes eachrefined probability distribution L_(i), corresponding to each instantJ_(i), 1≦i≦F, as a weighted average of:

-   -   i. the corresponding unrefined probability distribution V_(i),        and    -   ii. all available temporally-extrapolated probability        distributions D_(i,j), j≠i:

$\begin{matrix}{L_{i} = \frac{V_{i} + {\sum\limits_{j \neq i}\left\lbrack {\alpha^{{j - i}} \cdot D_{i,j}} \right\rbrack}}{1 + {\sum\limits_{j \neq i}\alpha^{{j - i}}}}} & \left( {{Eq}.\mspace{14mu} 10} \right)\end{matrix}$wherein α is a constant, 0<α<1, that acts as an “aging factor” thatweights less temporally-extrapolated probability distributions moreheavily that more temporally-extrapolated probability distributionsbecause of the more temporally-extrapolated probabilities distributionsare less likely to be correct than the less temporally-extrapolatedprobability distributions. For example, when i=4 and F=5, Equation 10 inexpanded form yields:

$\begin{matrix}{L_{4} = \frac{V_{4} + {\alpha \cdot D_{4,3}} + {\alpha \cdot D_{4,5}} + {\alpha^{2} \cdot D_{4,2}} + {\alpha^{3} \cdot D_{4,1}}}{1 + {2\alpha} + \alpha^{2} + \alpha^{3}}} & \left( {{Eq}.\mspace{14mu} 11} \right)\end{matrix}$

Defining D_(i,i)=V_(i), Equation 10 can be expressed in a simpler formthat is particularly convenient for computer processing:

$\begin{matrix}{L_{i} = \frac{\sum\limits_{j = 1}^{F}\left\lbrack {\alpha^{{j - i}} \cdot D_{i,j}} \right\rbrack}{\sum\limits_{j = 1}^{F}\alpha^{{j - i}}}} & \left( {{Eq}.\mspace{14mu} 12} \right)\end{matrix}$

In accordance with process 1305, location server 214 generates anestimate of the location of wireless terminal 201 at one or moreinstants J_(i) based on the maximum likelihood function of L_(i). (Aswill be appreciated by those skilled in the art, after reading thisdisclosure, in some other embodiments of the present invention anestimate might be generated from probability distribution L_(i) usinganother function or method.)

In accordance with process 1306, location server 214 provides theestimate(s) of the location of wireless terminal 201 generated inprocess 1305 to location client 213, in well-known fashion.

It is to be understood that the above-described embodiments are merelyillustrative of the present invention and that many variations of theabove-described embodiments can be devised by those skilled in the artwithout departing from the scope of the invention. It is thereforeintended that such variations be included within the scope of thefollowing claims and their equivalents.

1. A method comprising: (1) receiving (i) a first measured temporaldifference for a first pair of multipath components of a first signalthat is processed by a wireless terminal and (ii) a second measuredtemporal difference for a second pair of multipath components of asecond signal that is processed by the wireless terminal; and (2)estimating the location of the wireless terminal based on the firstmeasured temporal difference and the second measured temporaldifference; wherein (2) estimating the location of the wireless terminalcomprises: (2.1) comparing the first measured temporal difference to:(i) a first expected temporal difference of the first pair of multipathcomponents of the first signal when the wireless terminal is at a firstlocation, and (ii) a second expected temporal difference of the firstpair of multipath components of the first signal when the wirelessterminal is at a second location; and (2.2) comparing the secondmeasured temporal difference to: (i) a first expected temporaldifference of the second pair of multipath components of the secondsignal when the wireless terminal is at the first location, and (ii) asecond expected temporal difference of the second pair of multipathcomponents of the second signal when the wireless terminal is at thesecond location.
 2. A method comprising: (1) receiving (i) a firstmeasured temporal difference for a first pair of multipath components ofa first signal that is processed by a wireless terminal at a first timeT₁ and (ii) a second measured temporal difference for a second pair ofmultipath components of a second signal at a second time T₂, wherein thefirst time does not equal the second time; and (2) estimating thelocation of the wireless terminal at the second time based on (i) thefirst measured temporal difference, (ii) the second measured temporaldifference, and (iii) an estimate of the probability that the wirelessterminal in the location at a time T will still be in the location at alater time T+Δt; wherein (2) estimating the location of the wirelessterminal comprises: (2.1) comparing the first measured temporaldifference to: (i) a first expected temporal difference of the firstpair of multipath components of the first signal when the wirelessterminal is at a first location at the first time T₁, and (ii) a secondexpected temporal difference of the first pair of multipath componentsof the first signal when the wireless terminal is at a second locationat the first time T₁; and (2.2) comparing the second measured temporaldifference to: (i) a first expected temporal difference of the secondpair of multipath components of the second signal when the wirelessterminal is at the first location at the first time T₂, and (ii) asecond expected temporal difference of the second pair of multipathcomponents of the second signal when the wireless terminal is at thesecond location at the first time T₂.
 3. A method comprising: (1)receiving (i) a first pair of measured temporal differences for a firsttriplet of multipath components of a first signal that is processed by awireless terminal and (ii) a second pair of measured temporaldifferences for a second triplet of multipath components of a secondsignal that is processed by the wireless terminal; and (2) estimatingthe location of the wireless terminal based on the first pair ofmeasured temporal differences and the second pair of measured temporaldifferences; wherein (2) estimating the location of the wirelessterminal comprises: (2.1) comparing the first pair of measured temporaldifferences to: (i) a first pair of expected temporal differences of thefirst triplet of multipath components of the first signal when thewireless terminal is at a first location, and (ii) a second pair ofexpected temporal differences of the first triplet of multipathcomponents of the first signal when the wireless terminal is at a secondlocation; and (2.2) comparing the second pair of measured temporaldifferences to: (i) a first pair of expected temporal differences of thesecond triplet of multipath components of the second signal when thewireless terminal is at the first location, and (ii) a second pair ofexpected temporal differences of the second triplet of multipathcomponents of the second signal when the wireless terminal is at thesecond location.
 4. A method comprising: (1) receiving (i) a first pairof measured temporal differences for a first triplet of multipathcomponents of a first signal that is processed by a wireless terminal ata first time T₁ and (ii) a second pair of measured temporal differencesfor a second triplet of multipath components of a second signal at asecond time T₂, wherein the first time does not equal the second time;and (2) estimating the location of the wireless terminal at the secondtime based on (i) the first pair of measured temporal differences, (ii)the second pair of measured temporal differences, and (iii) an estimateof the probability that the wireless terminal in the location at a timeT will still be in the location at a later time T+Δt; wherein (2)estimating the location of the wireless terminal comprises: (2.1)comparing the first pair of measured temporal differences to: (i) afirst expected temporal difference of the first triplet of multipathcomponents of the first signal when the wireless terminal is at a firstlocation at the first time T₁, and (ii) a second expected temporaldifference of the first triplet of multipath components of the firstsignal when the wireless terminal is at a second location at the firsttime T₁; and (2.2) comparing the second pair of measured temporaldifferences to: (i) a first expected temporal difference of the secondtriplet of multipath components of the second signal when the wirelessterminal is at the first location at the first time T₂, and (ii) asecond expected temporal difference of the second triplet of multipathcomponents of the second signal when the wireless terminal is at thesecond location at the first time T₂.
 5. A method comprising: (1)receiving (i) a first measured delay spread of a first signal that isprocessed by a wireless terminal and (ii) a second measured delay spreadof a second signal that is processed by the wireless terminal; and (2)estimating the location of the wireless terminal based on the firstmeasured delay spread and the second measured delay spread; wherein (2)estimating the location of the wireless terminal comprises: (2.1)comparing the first measured delay spread to: (i) a first expected delayspread of the first signal when the wireless terminal is at a firstlocation, and (ii) a second expected delay spread of the first signalwhen the wireless terminal is at a second location; and (2.2) comparingthe second measured delay spread to: (i) a first expected delay spreadof the second signal when the wireless terminal is at the firstlocation, and (ii) a second expected delay spread of the second signalwhen the wireless terminal is at the second location.
 6. A methodcomprising: (1) receiving (i) a first measured delay spread of a firstsignal that is processed by a wireless terminal at a first time T₁ and(ii) a second measured delay spread of a second signal at a second timeT₂, wherein the first time does not equal the second time; and (2)estimating the location of the wireless terminal at the second timebased on (i) the first measured delay spread, (ii) the second measureddelay spread, and (iii) an estimate of the probability that the wirelessterminal in the location at time a T will still be in the location at alater time T+Δt; wherein (2) estimating the location of the wirelessterminal comprises: (2.1) comparing the first measured delay spread to:(i) a first expected delay spread of the first signal when the wirelessterminal is at a first location at the first time T₁, and (ii) a secondexpected delay spread of the first signal when the wireless terminal isat a second location at the first time T₁; and (2.2) comparing thesecond measured delay spread to: (i) a first expected delay spread ofthe second signal when the wireless terminal is at the first location atthe first time T₂, and (ii) a second expected delay spread of the secondsignal when the wireless terminal is at the second location at the firsttime T₂.